1. University of British Columbia CPSC 314 Computer Graphics Jan-Apr 2008 Tamara Munzner http://www.ugrad.cs.ubc.ca/~cs314/Vjan2008 Transformations II Week 2, Fri Jan 18

2. 2 Assignments

3. 3 project 1 out today, due 6pm Wed Feb 6 projects will go out before we’ve covered all the material so you can think about it before diving in build mouse out of cubes and 4x4 matrices think cartoon, not beauty template code gives you program shell, Makefile http://www.ugrad.cs.ubc.ca/~cs314/Vjan2008/p1.tar.gz written homework 1 out Monday, due 1pm sharp Wed Feb 6 theoretical side of material

4. 4 Demo animal out of boxes and matrices

5. 5 Real Mice http://www.com.msu.edu/carcino/Resources/mouse.jpg http://www.naturephoto-cz.com/photos/andera/house-mouse-15372.jpg http://www.naturephoto-cz.com/photos/andera/house-mouse-13044.jpg http://www.scientificillustrator.com/art/wildlife/mouse.jpg http://www.dezeen.com/wp-content/uploads/2007/10/mouse-in-a-bottle_sq.jpg

6. 6 Think Cartoon

7. 7 Armadillos!

8. 8 Monkeys!

9. 9

10. 10 Giraffes!

11. 11 Giraffes!

12. 12 Kangaroos!

13. 13 Project 1 Advice do not model everything first and only then worry about animating interleave modelling, animation for each body part: add it, then jumpcut animate, then smooth animate discover if on wrong track sooner dependencies: can’t get anim credit if no model use body as scene graph root check from all camera angles

14. 14 Project 1 Advice finish all required parts before going for extra credit playing with lighting or viewing ok to use glRotate, glTranslate, glScale ok to use glutSolidCube, or build your own where to put origin? your choice center of object, range -.5 to +.5 corner of object, range 0 to 1

15. 15 Project 1 Advice visual debugging color cube faces differently colored lines sticking out of glutSolidCube faces make your cubes wireframe to see inside thinking about transformations move physical objects around play with demos Brown scenegraph applets

16. 16 Project 1 Advice smooth transition change happens gradually over X frames key click triggers animation one way: redraw happens X times linear interpolation: each time, param += (new-old)/30 or redraw happens over X seconds even better, but not required

17. 17 Project 1 Advice transitions safe to linearly interpolate parameters for glRotate/glTranslate/glScale do not interpolate individual elements of 4x4 matrix!

18. 18 Style you can lose up to 15% for poor style most critical: reasonable structure yes: parametrized functions no: cut-and-paste with slight changes reasonable names (variables, functions) adequate commenting rule of thumb: what if you had to fix a bug two years from now? global variables are indeed acceptable

19. 19 Version Control bad idea: just keep changing same file save off versions often after got one thing to work, before you try starting something else just before you do something drastic how? not good: commenting out big blocks of code a little better: save off file under new name p1.almostworks.cpp, p1.fixedbug.cpp much better: use version control software strongly recommended

20. 20 Version Control Software easy to browse previous work easy to revert if needed for maximum benefit, use meaningful comments to describe what you did “started on tail”, “fixed head breakoff bug”, “leg code compiles but doesn’t run” useful when you’re working alone critical when you’re working together many choices: RCS, CVS, svn/subversion all are installed on lab machines svn tutorial is part of next week’s lab

21. 21 Graphical File Comparison installed on lab machines xfdiff4 (side by side comparison) xwdiff (in-place, with crossouts) Windows: windiff http://keithdevens.com/files/windiff Macs: FileMerge in /Developer/Applications/Utilities

22. 22 Readings for Jan 16-25 FCG Chap 6 Transformation Matrices except 6.1.6, 6.3.1 FCG Sect 13.3 Scene Graphs RB Chap Viewing Viewing and Modeling Transforms until Viewing Transformations Examples of Composing Several Transformations through Building an Articulated Robot Arm RB Appendix Homogeneous Coordinates and Transformation Matrices until Perspective Projection RB Chap Display Lists

23. 23 Review: Event-Driven Programming main loop not under your control vs. procedural control flow through event callbacks redraw the window now key was pressed mouse moved callback functions called from main loop when events occur mouse/keyboard state setting vs. redrawing

24. 24 Review: 2D Rotation  (x, y) (x′, y′) x ′ = x cos(  ) - y sin(  ) y ′ = x sin(  ) + y cos(  ) counterclockwise, RHS

25. 25 Review: Shear, Reflection shear along x axis push points to right in proportion to height reflect across x axis mirror x y x y x x

26. 26 Review: 2D Transformations scaling matrixrotation matrix translation multiplication matrix?? vector addition matrix multiplication (x,y) (x′,y′)

27. 27 Review: Linear Transformations linear transformations are combinations of shear scale rotate reflect properties of linear transformations satisifes T(sx+ty) = s T(x) + t T(y) origin maps to origin lines map to lines parallel lines remain parallel ratios are preserved closed under composition

28. 28 3D Rotation About Z Axis glRotatef(angle,x,y,z); glRotatef(angle,0,0,1); general OpenGL command rotate in z

29. 29 3D Rotation in X, Y glRotatef(angle,1,0,0); around x axis: glRotatef(angle,0,1,0); around y axis:

30. 30 3D Scaling glScalef(a,b,c);

31. 31 3D Translation glTranslatef(a,b,c);

32. 32 3D Shear general shear to avoid ambiguity, always say "shear along in direction of "

33. 33 Summary: Transformationstranslate(a,b,c) scale(a,b,c)

34. 34 Undoing Transformations: Inverses (R is orthogonal)

35. 35 Composing Transformations

36. 36 Composing Transformations translation so translations add

37. 37 Composing Transformations scaling rotation so scales multiply so rotations add

38. 38 Composing Transformations Ta Tb = Tb Ta, but Ra Rb != Rb Ra and Ta Rb != Rb Ta translations commute rotations around same axis commute rotations around different axes do not commute rotations and translations do not commute

39. 39 Composing Transformations FhFhFhFh FWFWFWFW suppose we want

40. 40 Composing Transformations FhFhFhFh FWFWFWFW suppose we want FWFWFWFW FhFhFhFh Rotate(z,-90)

41. 41 Composing Transformations FhFhFhFh FWFWFWFW suppose we want FWFWFWFW FhFhFhFh Rotate(z,-90) FWFWFWFW FhFhFhFh Translate(2,3,0)

42. 42 Composing Transformations FhFhFhFh FWFWFWFW suppose we want FWFWFWFW FhFhFhFh Rotate(z,-90) FWFWFWFW FhFhFhFh Translate(2,3,0)

43. 43 Composing Transformations which direction to read? right to left interpret operations wrt fixed coordinates moving object left to right interpret operations wrt local coordinates changing coordinate system

44. 44 Composing Transformations which direction to read? right to left interpret operations wrt fixed coordinates moving object left to right interpret operations wrt local coordinates changing coordinate system OpenGL pipeline ordering!

45. 45 Composing Transformations which direction to read? right to left interpret operations wrt fixed coordinates moving object left to right interpret operations wrt local coordinates changing coordinate system OpenGL updates current matrix with postmultiply glTranslatef(2,3,0); glRotatef(-90,0,0,1); glVertexf(1,1,1); specify vector last, in final coordinate system first matrix to affect it is specified second-to-last OpenGL pipeline ordering!

46. 46 (2,1) (1,1) changing coordinate system moving object translate by (-1,0) Interpreting Transformations same relative position between object and basis vectors intuitive? OpenGL

47. 47 Matrix Composition matrices are convenient, efficient way to represent series of transformations general purpose representation hardware matrix multiply matrix multiplication is associative p′ = (T*(R*(S*p))) p′ = (T*R*S)*p procedure correctly order your matrices! multiply matrices together result is one matrix, multiply vertices by this matrix all vertices easily transformed with one matrix multiply

48. 48 Rotation About a Point: Moving Object FWFWFWFW translate p to origin rotate about p by : p by : rotate about origin translate p back

49. 49 Rotation: Changing Coordinate Systems same example: rotation around arbitrary center

50. 50 Rotation: Changing Coordinate Systems rotation around arbitrary center step 1: translate coordinate system to rotation center

51. 51 Rotation: Changing Coordinate Systems rotation around arbitrary center step 2: perform rotation

52. 52 Rotation: Changing Coordinate Systems rotation around arbitrary center step 3: back to original coordinate system

53. 53 General Transform Composition transformation of geometry into coordinate system where operation becomes simpler typically translate to origin perform operation transform geometry back to original coordinate system

54. 54 Rotation About an Arbitrary Axis axis defined by two points translate point to the origin rotate to align axis with z-axis (or x or y) perform rotation undo aligning rotations undo translation

55. Arbitrary Rotation arbitrary rotation: change of basis given two orthonormal coordinate systems XYZ and ABC A ’ s location in the XYZ coordinate system is (a x, a y, a z, 1),... transformation from one to the other is matrix R whose columns are A,B,C: Y Z X B C A Y Z X B C A (c x, c y, c z, 1) (a x, a y, a z, 1) (b x, b y, b z, 1)